We have determined oxygen binding curves from polarized optical absorption spectra of single crystals of human hemoglobin measured as a function of oxygen pressure. An analysis of the oxygen binding properties of the alpha and beta subunits in the crystal indicates that the observed Hill n close to 1.0 may arise from a compensation effect between inequivalent oxygen binding to the two types of subunits and a degree of cooperativity in the binding to the protein in the T quaternary structure. We have also studied the effects of photoselection on time-resolved spectra measured in partial-photolysis experiments using linearly polarized excitation and probe pulses. The ability to obtain isotropically averages spectra which are free of these effects has allowed the determination of the conformational and ligand binding kinetics of myoglobin and hemoglobin with unprecedented accuracy. We have also performed long molecular dynamics simulations to study heme reorientational motions in myoglobin. In these simulations the heme orientation and the protein backbone conformation explore different regions of their respective spaces in a correlated fashion. The simulations predict subnanosecond heme reorientational motions which account for about 30 percent of the reduction of the initial absorption anisotropy observed in partial photolysis experiments on myoglobin.